ELECTROMAGNETIC SCATTERING BY CONDUCTORS IN THE EARTH NEAR A LINE SOURCE OF CURRENT

Geophysics ◽  
1971 ◽  
Vol 36 (1) ◽  
pp. 101-131 ◽  
Author(s):  
Gerald W. Hohmann
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Line Source ◽  
Numerical Technique ◽  
The Body ◽  
Scale Model ◽  
Electromagnetic Response ◽  
Field Phase ◽  
Horizontal Magnetic Field ◽  
Depth Of Burial

A theoretical solution is developed for the electromagnetic response of a two‐dimensional inhomogeneity in a conductive half‐space, in the field of a line source of current. The solution is in the form of an integral equation, which is reduced to a matrix equation, and solved numerically for the electric field in the body. The electric and magnetic fields at the surface of the half‐space are found by integrating the half‐space Green’s functions over the scattering currents. One advantage of this particular numerical technique is that it is necessary to solve for scattering currents only in the conductor and not throughout the half‐space. The response of a thin, vertical conductor is studied in some detail. Because the only interpretational aids available previously were scale model results for conductors in free space, the results presented here should be useful in interpreting data and in designing new EM systems. As expected, anomalies decay rapidly as depth of burial is increased, due to attenuation in the conductive half‐space. Depth of exploration appears to be greatest for measurements of horizontal magnetic field phase, while vertical field phase is diagnostic of conductivity. Horizontal location and depth of burial are best determined through measurements of vertical or horizontal magnetic field amplitude.

Three‐dimensional transient electromagnetic responses for a grounded source

Geophysics ◽  
1986 ◽  
Vol 51 (11) ◽  
pp. 2117-2130 ◽  
Author(s):  
Brian M. Gunderson ◽  
Gregory A. Newman ◽  
Gerald W. Hohmann
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Time Derivative ◽  
Three Dimensional ◽  
The Body ◽  
Vertical Magnetic Field ◽  
Horizontal Magnetic Field ◽  
One Dimensional ◽  
Transient Electromagnetic ◽  
Electromagnetic Responses

When the current in a grounded wire is terminated abruptly, currents immediately flow in the Earth to preserve the magnetic field. Initially the current is concentrated near the wire, with a broad zone of return currents below. The electric field maximum broadens and moves downward with time. Currents are channeled into a conductive three‐dimensional body, resulting in anomalous magnetic fields. At early times, when the return currents are channeled into the body, the vertical magnetic field is less than the half‐space field on the far side of the body but is greater than the half‐space field between the source and the body. Later the current in the body reverses; the vertical field is enhanced on the far side of the body and decreased between the source and the body. The horizontal magnetic field has a well‐defined maximum directly over the body at late times, and is a better indicator of the position of the body. The vertical magnetic field and its time derivative change sign with time at receiver locations near the source if a three‐dimensional body is present. These sign reversals present serious problems for one‐dimensional inversion, because decay curves for a layered earth do not change sign. At positions away from the source, the decay curves exhibit no sign reversals—only decreases and enhancements relative to one‐dimensional decay curves. In such cases one‐dimensional inversions may provide useful information, but they are likely to result in fictitious layers and erroneous interpretations.

THE ELECTROMAGNETIC FIELDS OF A SUBTERRANEAN CYLINDRICAL INHOMOGENEITY EXCITED BY A LINE SOURCE

Geophysics ◽  
1972 ◽  
Vol 37 (6) ◽  
pp. 975-984 ◽  
Author(s):  
Allen Q. Howard
Keyword(s):  
Magnetic Field ◽  
Integral Equation ◽  
Line Source ◽  
Field Amplitude ◽  
Two Dimensional ◽  
Vertical Magnetic Field ◽  
Geophysical Prospecting ◽  
Field Phase ◽  
Horizontal Magnetic Field ◽  
Mine Rescue

The anomalous fields from a buried cylindrical inhomogeneity in an otherwise uniform half‐space are analyzed. The problem is rendered two‐dimensional by assuming that the uniform line source of current is parallel to the subsurface cylinder. The multipole scattered field coefficients are obtained from the numerical solution to the associated singular Fredholm integral equation of the second kind. The horizontal magnetic field amplitude, the vertical magnetic field phase, and the amplitude and phase of the ratio of horizontal to vertical magnetic fields are shown to be diagnostic of the location of the inhomogeneity. The results have possible applications to electromagnetic location in mine rescue operations and to geophysical prospecting.

THE EFFECT OF A DIPPING CONTACT ON THE BEHAVIOR OF THE ELECTROMAGNETIC FIELD

Geophysics ◽  
1972 ◽  
Vol 37 (2) ◽  
pp. 337-350 ◽  
Author(s):  
Richard G. Geyer
Keyword(s):  
Magnetic Field ◽  
Plane Waves ◽  
Skin Depth ◽  
Electromagnetic Response ◽  
Vertical Magnetic Field ◽  
Field Phase ◽  
Incident Plane ◽  
Electric And Magnetic Fields ◽  
Orthogonal Components ◽  
Integral Solutions

Theoretical solutions for the electromagnetic response of a dipping interface in the field of normally incident plane waves are given in the form of inverse Lebedev‐Kontorovich transforms. When the lateral resistivity contrast becomes very large, the resulting integral solutions simplify considerably and allow ready numerical evaluation. The amplitude response of the vertical magnetic field seems most diagnostic of the structural attitude of sloping interfaces, even though the vertical magnetic field phase appears relatively insensitive to dip changes compared to horizontal electric field phase. The disturbance in the homogeneity of the field caused by the presence of an inclined contact is postulated to be due to cylindrically diffused waves generated by the dipping interface and propagating along the earth’s surface. It would then seem that formulation of plane‐wave impedances from orthogonal components of the surface electric and magnetic fields would only be applicable at distances from the interface which are large relative to a skin depth in either layer. The results presented here should prove to be useful in detecting and defining sloping interfaces or in avoiding their effects.

The effect of a conductive half‐space on the transient electromagnetic response of a three‐dimensional body

Geophysics ◽  
1985 ◽  
Vol 50 (7) ◽  
pp. 1144-1162 ◽  
Author(s):  
William A. SanFilipo ◽  
Perry A. Eaton ◽  
Gerald W. Hohmann
Keyword(s):  
Half Space ◽  
Free Space ◽  
Eddy Currents ◽  
Three Dimensional ◽  
Vertical Component ◽  
The Body ◽  
Electromagnetic Response ◽  
Loop Current ◽  
Transient Electromagnetic ◽  
Space Response

The transient electromagnetic (TEM) response of a three‐dimensional (3-D) prism in a conductive half‐space is not always approximated well by three‐dimensional free‐space or two‐dimensional (2-D) conductive host models. The 3-D conductive host model is characterized by a complex interaction between inductive and current channeling effects. We numerically computed 3-D TEM responses using a time‐domain integral‐equation solution. Models consist of a vertical or horizontal prismatic conductor in conductive half‐space, energized by a rapid linear turn‐off of current in a rectangular loop. Current channeling, characterized by currents that flow through the body, is produced by charges which accumulate on the surface of the 3-D body and results in response profiles that can be much different in amplitude and shape than the corresponding response for the same body in free space, even after subtracting the half‐space response. Responses characterized by inductive (vortex) currents circulating within the body are similar to the response of the body in free space after subtracting the half‐space contribution. The difference between responses dominated by either channeled or vortex currents is subtle for vertical bodies but dramatic for horizontal bodies. Changing the conductivity of the host effects the relative importance of current channeling, the velocity and rate of decay of the primary (half‐space) electric field, and the build‐up of eddy currents in the body. As host conductivity increases, current channeling enhances the amplitude of the response of a vertical body and broadens the anomaly along the profile. For a horizontal body the shape of the anomaly is distorted from the free‐space anomaly by current channeling and is highly sensitive to the resistivity of the host. In the latter case, a 2-D response is similar to the 3-D response only if current channeling effects dominate over inductive effects. For models that are not greatly elongated, TEM responses are more sensitive to the conductivity of the body than galvanic (dc) responses, which saturate at a moderate resistivity contrast. Multicomponent data are preferable to vertical component data because in some cases the presence and location of the target are more easily resolved in the horizontal response and because the horizontal half‐space response decays more quickly than does the corresponding vertical response.

Effect of conductive host rock on borehole transient electromagnetic responses

Geophysics ◽  
1989 ◽  
Vol 54 (5) ◽  
pp. 598-608 ◽  
Author(s):  
Gregory A. Newman ◽  
Walter L. Anderson ◽  
Gerald W. Hohmann
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Time Derivative ◽  
The Body ◽  
Galvanic Current ◽  
Large Loop ◽  
Transient Electromagnetic ◽  
Electromagnetic Responses ◽  
Pass Through ◽  
The Magnetic Field

Transient electromagnetic (TEM) borehole responses of 3-D vertical and horizontal tabular bodies in a half‐space are calculated to assess the effect of a conductive host. The transmitter is a large loop at the surface of the earth, and the receiver measures the time derivative of the vertical magnetic field. When the host is conductive (100 Ω ⋅ m), the borehole response is due mainly to current channeled through the body. The observed magnetic‐field response can be visualized as due to galvanic currents that pass through the conductor and return in the half‐space. When the host resistivity is increased, the magnetic field of the conductor is influenced more by vortex currents that flow in closed loops inside the conductor. For a moderately resistive host (1000 Ω ⋅ m), the magnetic field of the body is caused by both vortex and galvanic currents. The galvanic response is observed at early times, followed by the vortex response at later times if the body is well coupled to the transmitter. If the host is very resistive, the galvanic response vanishes; and the response of the conductor is caused only by vortex currents. The shapes of the borehole profiles change considerably with changes in the host resistivity because vortex and galvanic current distributions are very different. When only the vortex response is observed, it is easy to distinguish vertical and horizontal conductors. However, in a conductive host where the galvanic response is dominant, it is difficult to interpret the geometry of the body; only the approximate location of the body can be determined easily. For a horizontal conductor and a single transmitting loop, only the galvanic response enables one to determine whether the conductor is between the transmitter and the borehole or beyond the borehole. A field example shows behavior similar to that of our theoretical results.

Two‐dimensional transient electromagnetic responses

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2849-2861 ◽  
Author(s):  
Jopie I. Adhidjaja ◽  
Gerald W. Hohmann ◽  
Michael L. Oristaglio
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Time Domain ◽  
The Body ◽  
Two Dimensional ◽  
Total Field ◽  
Secondary Field ◽  
Field Solution ◽  
Transient Electromagnetic ◽  
Simple Boundary

The time‐domain electromagnetic (TEM) modeling method of Oristaglio and Hohmann is reformulated here in terms of the secondary field. This finite‐difference method gives a direct, explicit time‐domain solution for a two‐dimensional body in a conductive earth by advancing the field in time with DuFort‐Frankel time‐differencing. As a result, solving for the secondary field, defined as the difference between the total field and field of a half‐space, is not only more efficient but is also simpler and eliminates several problems inherent in the solution for the total field. For example, because the secondary field varies slowly both in space and time, it can be modeled on a coarse grid with large time steps. In addition, for a simple body the field is local; therefore, because the field can be assumed to satisfy a simple boundary condition in the earth computation is greatly simplified. Our tests show that for the same accuracy, the secondary‐field solution is roughly five times faster than the total‐field solution. We compute and analyze the magnetic field impulse response for a suite of models, most of which consist of a thin body embedded in a conductive half‐space—with or without overburden. The results indicate the conductive half‐space will both delay and attenuate the response of the body and even obscure it if the conductivity contrast is small. The results also suggest that the conductive host can alter the decay rate of the response of the body from its free‐space counterpart. Our results for multiple bodies illustrate the importance of early‐time measurements to obtain resolution, particularly for measurements of the horizontal magnetic field. The vertical magnetic field, however, can be used to infer the dip direction of a dipping body by studying the migration of the crossover. The results for models which include overburden show that the effect of a conductive overburden, in addition to the half‐space effect, is to delay the response of the body, because the primary current initially tends to concentrate and slowly diffuse through the overburden, and does not reach the body until later time. This effect also complicates the early‐times profiles, becoming more severe as the conductivity of the overburden is increased.

QUASI‐STATIC TRANSIENT RESPONSE OF A CONDUCTING PERMEABLE SPHERE

Geophysics ◽  
1969 ◽  
Vol 34 (5) ◽  
pp. 789-792 ◽  
Author(s):  
James R. Wait ◽  
Kenneth P. Spies
Keyword(s):  
Magnetic Field ◽  
Eddy Currents ◽  
Massive Sulfide ◽  
The Body ◽  
Electromagnetic Response ◽  
Transient Solution ◽  
Time Harmonic ◽  
Time Domain Electromagnetic ◽  
Permeable Sphere ◽  
Drill Holes

When a conducting body is immersed in a time‐varying magnetic field, eddy currents are induced. These, in turn, produce a secondary magnetic field which may be detected by an observer external to the sphere. It has been demonstrated that a measurement of the external field can be used to estimate the conductivity of the body if certain assumptions are valid. For example, Ward (1953) has shown that the conductivity and permeability of geological core specimens from diamond drill holes may be determined by examining the frequency dependence of the time‐harmonic response of the specimen. In principle, the same information should also be available from the time response of the specimen for a suddenly applied magnetic field (Wait, 1951). In this paper, we wish to discuss the transient solution when a homogeneous conducting sphere is under the influence of a transient magnetic field. Also, as suggested earlier by Wait (1951), the actual time‐domain electromagnetic response of a massive sulfide body should exhibit features akin to this transient solution. Thus, the results should have application in mining geophysics. We consider both a nonpermeable and a permeable sphere, using a different approach for each. Because the former is a special case of the latter, a consistency check is obtained.

Two-dimensional oscillation of convection roll in a finite liquid metal layer under a horizontal magnetic field

2021 ◽  
Vol 911 ◽  
Author(s):  
Y. Tasaka ◽  
T. Yanagisawa ◽  
K. Fujita ◽  
T. Miyagoshi ◽  
A. Sakuraba
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Metal Layer ◽  
Two Dimensional ◽  
Horizontal Magnetic Field ◽  
Convection Roll

Abstract

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